CN103099637B - Image reconstruction method for dual panel position-emission tomography (PET) detector - Google Patents
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Abstract
The invention relates to an image reconstruction method for a dual panel position-emission tomography (PET) detector. The image reconstruction method for the dual panel PET detector comprises the following steps: conducting simulation on image process of a dual panel PET detection structure by using simulation software; recording line of response (LOR) information corresponding to all coincidence events and voxels where annihilation events lay; judging the type of one coincidence event according to positions of photon pairs in the annihilation events, considering the coincidence event as a true coincidence event if the occurring positions of the pair of photons corresponding to the coincidence event are consistent, considering the coincidence event as a random coincidence event if the occurring positions are inconsistent and removing the random coincidence event; expanding the range of the voxels; obtaining a compressed system response matrix through calculation by using symmetry of the structure the dual panel PET detector; reconstructing an image by using the obtained system response matrix. The image reconstruction method for the dual panel PET detector can be widely in the image reconstruction of the PET detector with the dual panel PET detection structure.
Description
Technical field
The present invention relates to a kind of image rebuilding method, particularly about a kind of image rebuilding method for two dull and stereotyped PET detectors.
Background technology
Positron emission tomography (Positron Emission Tomography, PET) is a kind of noninvasive in body functional imaging technology, is widely used in clinical examination and biological study.Conventional P ET detector adopts annular detecting structure to obtain the complete sampling of angle mostly, in order to reduce costs and the complexity of system, in some specific application, also there is researcher to propose two dull and stereotyped PET detecting structures, in improving sensitivity and spatial resolution, can also significantly reduce costs.Positron emission mammary gland fault imaging (Positron Emission Mammography, the PEM) technology of the two dull and stereotyped PET detecting structures of application is exactly wherein typically to apply, and can distribute and carry out fault imaging the radioactive substance in mammary gland with it.In addition, two dull and stereotyped PET detecting structures can also be used for toy to carry out imaging.
The sampling angle that two dull and stereotyped PET detecting structures obtain is limited, makes traditional analytic reconstruction algorithm no longer applicable; And, because two dull and stereotyped PET detecting structure middle plateform spacing are less, therefore there is significant reaction depth effect (Depth-Of-Interaction, DOI).These two kinds of factors all make system carry out accurate modeling and use iterative algorithm to rebuild very necessary.System response matrix (System Response Matrix, SRM) as the mathematical description of the imaging process of system, its importance is self-evident, system response matrix can pass through analytic method, Monte Carlo (Monte Carlo, MC) emulation, experimental technique or wherein several combining are obtained, wherein, analytic method is difficult to describe the physical factor including DOI, experimental technique needs to have an actual system, and to having relatively high expectations of experiment condition, operate also relative complex.By contrast, Monte Carlo method application is comparatively flexible, but the intrinsic statistical property of DSMC makes the system response matrix obtaining be subject to effect of noise; In addition, the scale of system response matrix is often very large, be difficult to whole system response matrix to call in internal memory, above-mentioned factors influence the application of DSMC in actual image reconstruction.The people such as ChienMin Kao utilize the symmetry of dull and stereotyped detecting structure to compress system response matrix, obtain good effect, but in the time of emulation, need in advance dull and stereotyped PET detector be expanded, thereby make simulation process become complicated, and affect the raising of compression factor.
Summary of the invention
For the problems referred to above, the object of this invention is to provide a kind of image rebuilding method for two dull and stereotyped PET detectors, simulation process is simple, and can utilize symmetry effectively to compress system response matrix.
For achieving the above object, the present invention takes following technical scheme: a kind of image rebuilding method for two dull and stereotyped PET detectors, it comprises the following steps: 1) the dull and stereotyped PET detecting structure of a pair of is set, it is by a upper flat plate detector with once flat panel detector is parallel just to forming, and the region between described upper flat plate detector and lower flat panel detector is effective imaging region; 2) utilize simulation software to carry out emulation to the imaging process of two dull and stereotyped PET detecting structures, record all voxels that meet LOR information corresponding to event and annihilation event place; 3) judge meeting event type according to the right position of gammaphoton in annihilation event, if it is consistent to meet the position of a pair of gammaphoton generation corresponding to event, think that this meets event is true coincidence event, if position is inconsistent, think that this time meeting event is random coincidence event, and random coincidence event is rejected; 4) voxel scope is expanded; 5) utilize the symmetry of two dull and stereotyped PET panel detector structures to calculate the system response matrix of compression; 6) utilize the system response matrix obtaining to rebuild image.
The symmetry of the two dull and stereotyped PET panel detector structures of described step 5) utilization calculates the system response matrix of compression, comprises the following steps: 1. determine according to symmetry principle the combination that all LOR of required consideration and all voxels of required consideration form; 2. the LOR and the voxel " combination " that meet the corresponding LOR of event and voxel and carry out translation, upset or coordinate exchange simultaneously and make its required consideration described in belonging to 1. that do not belong to combinations thereof that during to emulation, obtain, by LOR after translation, upset or coordinate exchange, overlap with the LOR that 1. described needs are considered, and corresponding voxel is after same operation, also can overlap with the 1. described voxel of considering that needs; 3. calculate the meansigma methods that meets event number that above-mentioned each " combination " comprises, and using this meansigma methods corresponding element value in system response matrix; 4. according to the threshold value of setting, the element that meets event deficiency is set to zero; 5. with the form storage system response matrix of sparse matrix.
1. described step determines according to symmetry principle the combination that all LOR of required consideration and all voxels of required consideration form, comprise the following steps: a) along minor axis and the long axis direction of dull and stereotyped PET detector, crystal is numbered, for line number and row number, upper flat plate detector and lower flat panel detector are numbered simultaneously, by upper, lower flat panel detector respectively label is I and II or by upper, lower flat panel detector is numbered respectively II and I, according to the symmetry principle of two dull and stereotyped PET detecting structures, the LOR of the crystal composition of selecting number minimum crystal of line number and row in flat panel detector II and all line numbers in flat panel detector I to be not more than to be listed as number, b), according to the plate overturning invariability of z direction, select the voxel comprising near the half imaging aspect of flat panel detector II within the scope of the rear voxel of expansion, c) all voxels that the LOR that above-mentioned steps a) is selected and above-mentioned steps b) are selected form the combination of some LOR and voxel.
During the system response matrix that described step 6) utilization is obtained is rebuild image, search the element in the system response matrix that certain LOR and certain voxel are corresponding, concrete steps are: 1. first judge whether voxel belongs to the half imaging aspect near flat panel detector II, if voxel does not belong to the half imaging aspect near flat panel detector II, first by voxel and all upsets in the z-direction of corresponding LOR, make after upset, voxel belongs to the half imaging aspect near flat panel detector II; 2. analyzing LOR through which kind of operation can overlap with the LOR of the required consideration of 1. describing in described step 5), and voxel is done to same operation, the element of the system response matrix after the compression of the combination correspondence of the LOR obtaining after aforesaid operations and voxel, is the required element of searching.
The process that described step 4) is expanded voxel is: for the imaging aspect that is parallel to arbitrarily flat panel detector in effective areas imaging, first voxel scope is expanded along x positive direction, voxel number is in the x and y direction equated, ensure that voxel can not cross the border after the x and y coordinate of exchange voxel; Then voxel scope is expanded respectively to one times again along x negative direction and y negative direction respectively, ensures that voxel carries out x, the upset of y and z direction and carry out x and the translation of y direction after, voxel can not cross the border.
The present invention is owing to taking above technical scheme, it has the following advantages: 1, the present invention utilizes the symmetry of two dull and stereotyped PET detecting structures, reduce the quantity that meets line of response (LOR) that needs consideration, thereby realize the compression to system response matrix, compared with prior art, (compression factor is relevant to system scale can to obtain higher compression factor, if adopt 20 × 40 crystal array, compression factor is up to 262.3, by comparison, the compression factor that the method that the people such as Chi en-Min Kao adopt obtains is only 133.3), if the sparse property of recycling system response matrix, can further compress system response matrix.2, first the present invention expanded voxel scope before obtaining system response matrix, therefore can avoid utilizing after symmetry change, and the situation that part voxel exceeds effective areas imaging occurs.3, the present invention uses DSMC to carry out emulation to the imaging process of two dull and stereotyped PET detecting structures, obtain in emulation meet event number certain, can effectively improve the statistical property of system response matrix, improve its signal to noise ratio.4, the present invention is in the time using in conjunction with DSMC, compared with prior art, when emulation, do not need flat panel detector to expand, there is emulation advantage is easily set, can be widely used in the image reconstruction of the PET detector with two dull and stereotyped detecting structures.
Brief description of the drawings
Fig. 1 is two dull and stereotyped PET detecting structure schematic diagram of the present invention;
Fig. 2 is two symmetric two-dimensional representation of dull and stereotyped PET detecting structure of the present invention; Fig. 2 (a) is original LOR and the position view of voxel, Fig. 2 (b) is Fig. 2 (a) through the schematic diagram after translation in the x-direction, Fig. 2 (c) is Fig. 2 (a) through the schematic diagram after turning operation in the x-direction, and Fig. 2 (d) is Fig. 2 (a) through the schematic diagram after turning operation in the z-direction;
Fig. 3 illustrates in the present invention that voxel may exceed the schematic diagram of effective areas imaging after translation;
Fig. 4 is the principle schematic that the present invention expands voxel region;
Fig. 5 is the schematic diagram to the symmetric utilization of two dull and stereotyped PET detecting structure in the embodiment of the present invention.
Detailed description of the invention
Below in conjunction with drawings and Examples, the present invention is described in detail.
As shown in Figure 1, the present invention arranges the dull and stereotyped PET detecting structure of a pair of, it by a upper flat plate detector 1 with once flat panel detector 2 is parallel just to forming.Wherein, the array that upper flat plate detector 1 and lower flat panel detector 2 are all made up of some scintillation crystals, the region between upper flat plate detector 1 and lower flat panel detector 2 is effective imaging region.Effective imaging region is divided into the dull and stereotyped imaging aspect that several are parallel to upper flat plate detector 1 by the present invention, and the array that each imaging aspect is made up of some small cubes forms, and each small cubes is called a voxel; The present invention will meet line of response (Line of Response, LOR) and be defined as the line that connects respectively each crystal in upper and lower flat panel detector.
For convenience of description, set up as shown in Figure 1 a rectangular coordinate system, x axle is parallel to the minor axis (minor axis is the axis of symmetry that is parallel to minor face in upper flat plate detector) of upper flat plate detector 1, y axle is parallel to the major axis (major axis is the axis of symmetry that upper flat plate detector is parallel to long limit) of upper flat plate detector 1, the flat board of the vertical upper flat plate detector 1 of z axle, the initial point of coordinate system is positioned at the center of effective imaging region.The present invention represents upper flat plate detector 1 with subscript t, represents lower flat panel detector 2, the element in system response matrix with subscript b
for voxel
the gammaphoton sending is to by LOR
the probability receiving, wherein,
represent the centre coordinate of each crystal of crystal centering that LOR is corresponding.Because two dull and stereotyped PET detecting structures itself have symmetry, the value of the some elements in system response matrix is identical.In order to utilize the symmetry of two dull and stereotyped PET detecting structures, realize the compression to system response matrix, the present invention requires in the x and y direction, and the crystal pitch (center distance of adjacent crystal) in two dull and stereotyped PET detectors and the ratio of voxel size should be even number (such as 2,4 etc.).The symmetry principle of two dull and stereotyped PET detecting structures is described below:
(1) along the translation invariance of x and y direction: by crystal, the combination of (crystal is to forming a LOR) and voxel is moved along x and y direction simultaneously, and when the integral multiple that mobile distance is crystal pitch, crystal after translation to the combination of voxel with without the crystal of translation to remaining unchanged with the value of corresponding element in system response matrix that is combined in of voxel, that is:
In formula,
and m
xand m
yall integral multiples of crystal pitch.
(2) along x, the plate overturning invariability of y and z direction: by crystal to overturn along a direction with the combination of voxel simultaneously, through upset after crystal to the combination of voxel with without upset crystal to remaining unchanged with the value of corresponding element in system response matrix that is combined in of voxel, make R
x, R
yand R
zrepresent respectively along x, the turning operation of y and z direction, plate overturning invariability is:
(3) coordinate of x and y direction exchange invariance: by crystal to exchange with x and the y coordinate of the combination of voxel simultaneously, crystal after coordinate transform to the combination of voxel with without conversion crystal to remaining unchanged with the value of corresponding element in system response matrix that is combined in of voxel, make S represent the swap operation of x and y coordinate:
As shown in Figure 2, in order to further illustrate the symmetry of above-mentioned two dull and stereotyped PET panel detector structures, represent with solid black rectangle the crystal pair that LOR is corresponding, solid black blockage represents voxel, an element of the combination correspondence system response matrix of LOR and voxel, as shown in Fig. 2 (b), the combination of LOR and voxel is simultaneously along the translation of x direction, the combination of LOR and voxel while upset in the x-direction as shown in Figure 2 (c), the combination of LOR and voxel while upset in the z-direction as shown in Figure 2 (d) shows, the value that is combined in the corresponding element of system response matrix element after these three kinds of conversion equates with the value of the corresponding element that is combined in system response matrix element as shown in Figure 2 (a) shows.
Based on the symmetry of above-mentioned two dull and stereotyped PET detecting structures, the image rebuilding method for two dull and stereotyped PET detectors of the present invention, comprises the steps:
1, utilize simulation software to carry out emulation to the imaging process of two dull and stereotyped PET detecting structures, record all voxels that meet LOR information corresponding to event and annihilation event place.
When two dull and stereotyped PET detecting structures are carried out to emulation, can select according to the actual requirements suitable simulation software, not limit at this.Embodiments of the invention adopt GATE (Geant4Appl icat ion for Tomographic Emission) as simulation software, GATE utilizes DSMC, can be used for emulation as several physical such as DOI effects, in two dull and stereotyped PET detecting structures, DOI effect is the most remarkable on the impact of picture quality, therefore, in the emulation of the embodiment of the present invention, only consider DOI effect, and ignore positron free path, the non-colinear that gammaphoton is right, other physical effects such as system dead time, concrete simulation process is:
To in whole effective imaging region, be full of the radioactive substance of activity homogeneous, radioactive source type adopts back-to-back gammaphoton pair.In PET imaging, β+decay occurs radionuclide will emit a positron, positron is buried in oblivion with the electronics in tissue, can produce the contrary gammaphoton pair of a pair of direction of motion, if a pair of gammaphoton is detected within the extremely short time by a pair of crystal of upper flat plate detector 1 and lower flat panel detector 2 respectively, be referred to as to meet event.In simulation process, record meets the position at LOR information corresponding to event and annihilation event place, by analysis meet LOR information corresponding to event can learn gammaphoton to by any bar LOR(which to crystal) survey and obtain; And by analyzing the position of annihilation event generation, can know the voxel at annihilation event place.
2, judge meeting event type according to the right position of gammaphoton in annihilation event, if it is consistent to meet the position of a pair of gammaphoton generation corresponding to event, think that this meets event is true coincidence event, if position is inconsistent, think that this time meeting event is random coincidence event, and random coincidence event is rejected.
In order to reduce as far as possible the random coincidence event producing in simulation process, obtain true coincidence event as much as possible, should the activity of radioactive substance be arranged relatively lowly on the one hand, should acquisition time be arranged longly on the other hand.The true coincidence event that emulation obtains is more, and the statistical property of the final system response matrix obtaining is also just better.But true coincidence event is not The more the better, first, the true coincidence event that obtain is more, and required simulation time is longer; In addition, increasing of true coincidence event reduces the sparse property of system response matrix, thereby it is elongated to make to rebuild required time, therefore, can need to carry out according to the actual requirements choose reasonable.
3, as shown in Figure 3, for fear of utilizing symmetry change rear section voxel to exceed effective areas imaging, need to expand voxel scope, the detailed process of expansion is: as shown in Figure 4, for the imaging aspect that is parallel to arbitrarily flat panel detector in effective areas imaging, O is zero, OC is parallel to x axle, OA is parallel to y axle, suppose that effective imaging region adopts rectangle OABC to represent, first voxel scope is expanded to square OADE along x positive direction, voxel number is in the x and y direction equated, ensure after the x and y coordinate of exchange voxel, voxel can not cross the border, then voxel scope is expanded respectively to one times again along x negative direction and y negative direction respectively, expands to square DFGH, ensure that voxel carries out x, the upset of y and z direction and carry out x and the translation of y direction after, voxel can not cross the border.
4, utilize the symmetry of two dull and stereotyped PET panel detector structures to calculate the system response matrix of compression, comprise the following steps:
1. all LOR and the combination of expanding all voxels formations of required consideration within the scope of rear voxel that determine required consideration according to symmetry principle, concrete steps are:
A) along minor axis and the long axis direction of dull and stereotyped PET detector, crystal is numbered, be respectively line number and row number, upper flat plate detector and lower flat panel detector are numbered simultaneously, in embodiments of the invention by upper, lower flat panel detector respectively label is I and II, according to the symmetry principle of two dull and stereotyped PET detecting structures, the LOR(of the crystal composition of selecting number minimum crystal of line number and row in flat panel detector II and all line numbers in flat panel detector I to be not more than to be listed as number also can be by upper, lower flat panel detector is numbered respectively II and I, process is identical, do not repeat them here),
B), according to the plate overturning invariability of z direction, select within the scope of the rear voxel of expansion near the voxel in the half imaging aspect of flat panel detector II.
C) all voxels that the LOR that above-mentioned steps a) is selected and above-mentioned steps b) are selected form the combination of some LOR and voxel.
As shown in Figure 5, the crystal array of the present invention taking 4 × 8 further describes said process as example: the crystal array of supposing two dull and stereotyped PET detecting structures adopts vector (n, m) to represent, and n and m represent respectively line number and the row number of crystal array, i.e. connection (n
t, m
t) and (n
b, m
b) form a LOR, if definition line poor be Δ n=n
t-n
b, row are poor is Δ m=m
t-m
b, the poor equal LOR of and row poor for row, according to translation invariance and the plate overturning invariability of x and y direction, only need to consider one of them: with in connection flat panel detector II (1
b, 1
b) and the LOR of each crystal of the flat panel detector I response to all voxels, if consider the coordinate exchange invariance of x and y coordinate, only need to consider to connect (1
b, 1
b) and flat panel detector I as the response of the LOR of the crystal indicating with Lycoperdon polymorphum Vitt in Fig. 5 (line number that Lycoperdon polymorphum Vitt indicates in crystal is less than or equal to row number) to all voxels, if consider again the plate overturning invariability of z direction, only need to consider the imaging plane of half, consider " combination " of the voxel of the half imaging aspect of close flat panel detector II.
2. the LOR and the voxel " combination " that meet the required consideration of event described in may not belonging to 1. that during due to emulation, obtain, therefore needing that these are met to LOR corresponding to event and voxel carries out translation, upset or coordinate exchange simultaneously and makes its LOR of required consideration and " combination " of voxel described in belonging to 1., by LOR after translation, upset or coordinate exchange, overlap with the LOR that 1. described needs are considered, and corresponding voxel is after same operation, also can overlap with the 1. described voxel of considering that needs.
3. calculate the meansigma methods that meets event number that above-mentioned each " combination " comprises, and using this meansigma methods corresponding element value in system response matrix.
4. according to the threshold value of setting, the element that meets event number deficiency is set to zero, can improves like this statistical property of system response matrix, be also conducive to reduce and rebuild required time, threshold value can be determined according to actual needs, not limit at this.
5. because neutral element number in system response matrix is far more than nonzero element number, therefore carry out storage system response matrix with the form of sparse matrix.
5, utilize the system response matrix obtaining to rebuild image.
Conventionally in iterative reconstruction algorithm, operation the most consuming time is projection operation and back projection's operation, no matter be projection operation or back projection's operation, all need by utilizing symmetry principle to travel through whole system response matrix, if need to search the element in the system response matrix that certain LOR and certain voxel are corresponding, concrete steps are as follows:
1) first judge whether voxel belongs to the half imaging aspect near flat panel detector II, if voxel does not belong to the half imaging aspect near flat panel detector II, first by voxel and all upsets in the z-direction of corresponding LOR, make after upset, voxel belongs to the half imaging aspect near flat panel detector II.
2) analyze LOR through which kind of operation (translation, upset, coordinate exchange or wherein several combination) can with step 4 1. in the LOR of the required consideration described overlap, and voxel is done to same operation.The element that obtains the system response matrix after the compression of combination correspondence of LOR and voxel after aforesaid operations, is the required element of searching.
The system response matrix that utilization is read, and by existing method for reconstructing, image is rebuild, process of reconstruction repeats no more, and image rebuilding method can adopt conventional iterative reconstruction algorithm or rebuild through the special iterative reconstruction algorithm of optimizing, and is not restricted at this.
The various embodiments described above are only for illustrating the present invention, and wherein each step of method etc. all can change to some extent, and every equivalents of carrying out on the basis of technical solution of the present invention and improvement, all should not get rid of outside protection scope of the present invention.
Claims (4)
1. for an image rebuilding method for two dull and stereotyped PET detectors, it comprises the following steps:
1) the dull and stereotyped PET detecting structure of a pair of is set, it is by a upper flat plate detector with once flat panel detector is parallel just to forming, and the region between described upper flat plate detector and lower flat panel detector is effective imaging region;
2) utilize simulation software to carry out emulation to the imaging process of two dull and stereotyped PET detecting structures, record all voxels that meet LOR information corresponding to event and annihilation event place; Wherein, LOR, for meeting line of response, specifically refers to the line that connects respectively each crystal in upper and lower flat panel detector;
3) judge meeting event type according to the right position of gammaphoton in annihilation event, if it is consistent to meet the position of a pair of gammaphoton generation corresponding to event, think that this meets event is true coincidence event, if position is inconsistent, think that this time meeting event is random coincidence event, and random coincidence event is rejected;
4) voxel scope is expanded, concrete expansion process is: for the imaging aspect that is parallel to arbitrarily flat panel detector in effective areas imaging, first voxel scope is expanded along x positive direction, voxel number is in the x and y direction equated, ensure that voxel can not cross the border after the x and y coordinate of exchange voxel; Then voxel scope is expanded respectively to one times again along x negative direction and y negative direction respectively, ensures that voxel carries out x, the upset of y and z direction and carry out x and the translation of y direction after, voxel can not cross the border;
5) utilize the symmetry of two dull and stereotyped PET panel detector structures to calculate the system response matrix of compression;
6) utilize the system response matrix obtaining to rebuild image.
2. a kind of image rebuilding method for two dull and stereotyped PET detectors as claimed in claim 1, is characterized in that: described step 5) utilize the symmetry of two dull and stereotyped PET panel detector structures to calculate the system response matrix of compression, comprise the following steps:
1. determine according to symmetry principle the combination that all LOR of required consideration and all voxels of required consideration form;
2. the LOR and the voxel " combination " that meet the corresponding LOR of event and voxel and carry out translation, upset or coordinate exchange simultaneously and make its required consideration described in belonging to 1. that do not belong to combinations thereof that during to emulation, obtain, by LOR after translation, upset or coordinate exchange, overlap with the LOR that 1. described needs are considered, and corresponding voxel is after same operation, also can overlap with the 1. described voxel of considering that needs;
3. calculate the meansigma methods that meets event number that above-mentioned each " combination " comprises, and using this meansigma methods corresponding element value in system response matrix;
4. according to the threshold value of setting, the element that meets event deficiency is set to zero;
5. with the form storage system response matrix of sparse matrix.
3. a kind of image rebuilding method for two dull and stereotyped PET detectors as claimed in claim 2, it is characterized in that: 1. described step determines according to symmetry principle the combination that all LOR of required consideration and all voxels of required consideration form, and comprises the following steps:
A) along minor axis and the long axis direction of dull and stereotyped PET detector, crystal is numbered, for line number and row number, upper flat plate detector and lower flat panel detector are numbered simultaneously, by upper and lower flat panel detector respectively label be I and II or upper and lower flat panel detector be numbered respectively to II and I, according to the symmetry principle of two dull and stereotyped PET detecting structures, the LOR of the crystal composition of selecting number minimum crystal of line number and row in flat panel detector II and all line numbers in flat panel detector I to be not more than to be listed as number;
B), according to the plate overturning invariability of z direction, select the voxel comprising near the half imaging aspect of flat panel detector II within the scope of the rear voxel of expansion;
C) all voxels that the LOR that above-mentioned steps a) is selected and above-mentioned steps b) are selected form the combination of some LOR and voxel.
4. a kind of image rebuilding method for two dull and stereotyped PET detectors as claimed in claim 3, it is characterized in that: described step 6) utilize during the system response matrix that obtains rebuilds image, search the element in the system response matrix that certain LOR and certain voxel are corresponding, concrete steps are:
1. first judge whether voxel belongs to the half imaging aspect near flat panel detector II, if voxel does not belong to the half imaging aspect near flat panel detector II, first by voxel and all upsets in the z-direction of corresponding LOR, make after upset, voxel belongs to the half imaging aspect near flat panel detector II;
2. analyze LOR through which kind of operation can with described step 5) in the LOR of required consideration that 1. describes overlap, and voxel is done to same operation, the element of the system response matrix after the compression of the combination correspondence of the LOR obtaining after aforesaid operations and voxel, is the required element of searching.
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